[Rd] Fastest non-overlapping binning mean function out there?

Martin Morgan mtmorgan at fhcrc.org
Wed Oct 3 22:50:07 CEST 2012

On 10/3/2012 6:47 AM, Martin Morgan wrote:
> On 10/02/2012 05:19 PM, Henrik Bengtsson wrote:
>> Hi,
>>
>> I'm looking for a super-duper fast mean/sum binning implementation
>> available in R, and before implementing z = binnedMeans(x y) in native
>> code myself, does any one know of an existing function/package for
>> this?  I'm sure it already exists.  So, given data (x,y) and B bins
>> bx[1] < bx[2] < ... < bx[B] < bx[B+1], I'd like to calculate the
>> binned means (or sums) 'z' such that z[1] = mean(x[bx[1] <= x & x <
>> bx[2]]), z[2] = mean(x[bx[2] <= x & x < bx[3]]), .... z[B].  Let's
>> assume there are no missing values and 'x' and 'bx' is already
>> ordered.  The length of 'x' is in the order of 10,000-millions.  The
>> number of elements in each bin vary.
>
> since x and bx are ordered (sorting x would be expensive), the C code seems
> pretty straight-forward and memory-efficient -- create a result vector as long
> as bx, then iterate through x accumulating n and it's sum until x[i] >= bx[i].
> (I think R's implementation of mean() actually pays more attention to numerical
> error, but with this much data...)
>
> library(inline)
> binmean <- cfunction(signature(x="numeric", bx="numeric"),
> "   int nx = Rf_length(x), nb = Rf_length(bx), i, j, n;

I'll take my solution back. The problem specification says that x has
10,000-millions of elements, so we need to use R-devel and

R_xlen_t nx = Rf_xlength(x), nb = Rf_xlength(bx), i, j, n;

but there are two further issues. The first is that on my system

p\$ gcc --version
gcc (Ubuntu/Linaro 4.6.3-1ubuntu5) 4.6.3

I have __SIZEOF_SIZE_T__ 8 but

(a) the test in Rinternals.h:52 is of SIZEOF_SIZE_T, which is undefined. I end
up with typedef int R_xlen_t (e.g., after R CMD SHLIB, instead of using the
inline package, to avoid that level of uncertainty) and then

>      SEXP ans = PROTECT(NEW_NUMERIC(nb));
>      double sum, *xp = REAL(x), *bxp = REAL(bx), *ansp = REAL(ans);
>      sum = j = n = 0;
>      for (i = 0; i < nx; ++i) {

(b) because nx is a signed type, and since nx > .Machine\$integer.max is
represented as a negative number, I don't ever iterate this loop. So I'd have to
be more clever if I wanted this to work on all platforms.

For what it's worth, Herve's solution is also problematic

> xx = findInterval(bx, x)
Error in findInterval(bx, x) : long vector 'vec' is not supported

A different strategy for the problem at hand would seem to involve iteration
over sequences of x, collecting sufficient statistics (n, sum) for each
iteration, and calculating the mean at the end of the day. This might also
result in better memory use and allow parallel processing.

Martin

>          while (xp[i] >= bxp[j]) {
>               ansp[j++] = n > 0 ? sum / n : 0;
>               sum = n = 0;
>          }
>          n += 1;
>          sum += xp[i];
>      }
>      ansp[j] = n > 0 ? sum / n : 0;
>      UNPROTECT(1);
>      return ans;
> ")
>
> with a test case
>
> nx <- 4e7
> nb <- 1e3
> x <- sort(runif(nx))
> bx <- do.call(seq, c(as.list(range(x)), length.out=nb))
>
>
>  > bx1 <- c(bx[-1], bx[nb] + 1)
>  > system.time(res <- binmean(x, bx1))
>     user  system elapsed
>    0.052   0.000   0.050
>
> Martin
>
>>
>> Thanks,
>>
>> Henrik
>>
>> ______________________________________________
>> R-devel at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>
>
>

--
Dr. Martin Morgan, PhD
Fred Hutchinson Cancer Research Center
1100 Fairview Ave. N.
PO Box 19024 Seattle, WA 98109